James Peebles, a Canadian astrophysicist received the Nobel Prize for his calculations regarding the universe appearing after the Big Bang. To be more precise, the calculations regarded the microwave background radiation, which is an echo of the Big Bang. Peebles is a theorist, he didn’t discover the microwave background radiation but in the 1960s he made some calculations which proved the existence of it in the universe. Some years later, scientists discovered the microwave background radiation and it was exactly how Peebles calculated!
Michel Mayor and Didier Queloz were given the other part of the prize for discovering planets orbiting similar to our Sun. Interestingly, the first planet which orbits a star outside the Solar System was discovered by prof. Wolszczan, a Polish scientist but it was Mayor and Queloz who figured out the way to find planets orbiting stars outside the Solar System.